Multipolar Intuitionistic Fuzzy Ideal in B-Algebras

Mathematics, 2020

In this paper, we discuss the notion of an m-polar fuzzy (normal) subalgebra in B-algebras and its related properties. We consider characterizations of an m-polar fuzzy (normal) subalgebra. We define the concept of an m-polar intuitionistic fuzzy (normal) subalgebra in a B-algebra, and we characterize the m-polar intuitionistic fuzzy (normal) subalgebra. Given an m-polar fuzzy set, we construct a simple m-polar fuzzy set and discuss on m-polar intuitionistic fuzzy subalgebras of B-algebras.

Cauchy, 2024

In this paper, we start with the concept of 𝐵-algebras, commutative 𝐵-algebras and fuzzy ideal in 𝐵-algebras. We also study about multipolar intuitionistic fuzzy ideal. We explain the notion of multipolar intuitionistic fuzzy positive implicative ideal in 𝐵-algebras and some characterizes. In addition, we examine some theorems and proportions which contain the conditions for a multipolar intuitionistic fuzzy set become a multipolar intuitionistic fuzzy positive implicative ideal in 𝐵-algebras. One of the result is a multipolar intuitionistic fuzzy set (ℓ ̂, 𝑠) over commutative 𝐵-algebra 𝑋 is a multipolar intuitionistic fuzzy positive implicative ideal (ℓ ̂, 𝑠) over commutative 𝐵-algebra 𝑋 if and only if (𝑥 * 𝑦) * 𝑧 = 0 implies ℓ ̂(𝑥) ≥ inf {ℓ ̂(𝑦), ℓ ̂(𝑧)} and 𝑠(𝑥) ≤ 𝑠𝑢𝑝{𝑠(𝑦), 𝑠(𝑧)}, for all 𝑥, 𝑦, 𝑧 ∈ 𝑋.

International journal of pure and applied mathematics, 2017

In papers [2, 3, 4, 5, 6] we studied the notion of fuzzy structures, fuzzy subalgebras, fuzzy ideals and L-fuzzy subalgebras and T-ideals of BP-Algebras. Motivated by the works of several researchers on Intuitionistic fuzzy structures on Algebras such as BCI, BCK, BG and BF algebras, in this paper we introduce the notion of Intuitionistic L-fuzzy ideals in BP-algebras. AMS Subject Classification: 03E72, 06F35, 03G25

Mathematics, 2020

In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzzy reflexive hyper BCK-ideal are introduced herein, and their relations and properties are investigated. These concepts are discussed in connection with the k-polar lower level set and the k-polar upper level set.

Transstellar Journal , 2019

In this paper, we introduce the concept of-intuitionistic fuzzy ideal and-intuitionistic fuzzy ideal and study their properties.

2000

Abstract. We consider the intuitionistic fuzzification of the concept of subalgebras and ideals in BCK-algebras, and investigate some of their properties. We introduce the notion of equivalence relations on the family of all intuitionistic fuzzy ideals of a BCK-algebra and investigate some related properties.

Malaya Journal of Matematik

In this paper, the idea of intuitionistic fuzzy soft subalgebras, intuitionistic fuzzy soft ideals, and intuitionistic fuzzy soft a-ideals of B-algebra are introduced with many associated properties interrogated. In connection to the intuitionistic fuzzy soft set theory, translations, extensions, and multiplications of intuitionistic fuzzy soft subalgebras, intuitionistic fuzzy ideals, and intuitionistic fuzzy a-ideals are introduced. Interconnected with intuitionistic fuzzy soft translations, intuitionistic fuzzy soft extensions, and intuitionistic fuzzy soft multiplications of intuitionistic fuzzy soft subalgebras, intuitionistic fuzzy soft ideals, and intuitionistic fuzzy soft a-ideals are investigated.

2010

In this paper, we introduce the concept of intuitionistic fuzzy H-ideals in BCK-algebras and investigate some of its properties. Mathematics Subject Classification: 03E72, 03F55, 03G25

International Journal of Mathematics and Mathematical Sciences, 2000

We consider the intuitionistic fuzzification of the concept of subalgebras and ideals in BCK-algebras, and investigate some of their properties. We introduce the notion of equivalence relations on the family of all intuitionistic fuzzy ideals of a BCK-algebra and investigate some related properties.